Isomorphisms of unitary matrix spaces

1983 ◽  
pp. 1-6
Author(s):  
Jonathan Arazy
Keyword(s):  
Unitary Matrix ◽  
Matrix Spaces

Local uniform and uniform convexity of non-commutative symmetric spaces of measurable operators

1992 ◽  
Vol 111 (2) ◽  
pp. 355-368 ◽  
Author(s):  
Vladimir I. Chilin ◽  
Andrei V. Krygin ◽  
Pheodor A. Sukochev
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Symmetric Spaces ◽  
Compact Operators ◽  
Uniform Convexity ◽  
Unitary Matrix ◽  
Matrix Space ◽  
Measurable Operators ◽  
Unitary Matrix Space ◽  
Matrix Spaces

Let E be a separable symmetric sequence space, and let CE be the unitary matrix space associated with E, i.e. the Banach space of all compact operators x on l2 so that s(x) E, with the norm , where are the s-numbers of x. One of the interesting subjects in the theory of the unitary matrix spaces is the clarification of correlation between the geometric properties of the spaces E and CE. A series of results in this direction related with the notions of type, cotype and uniform convexity of the spaces CE has been already obtained (see 13).

On p-convexity and q-concavity of unitary matrix spaces

1985 ◽  
Vol 8 (3) ◽  
pp. 295-313 ◽  
Author(s):  
Jonathan Arazy ◽  
Pei-Kee Lin
Keyword(s):  
Unitary Matrix ◽  
Matrix Spaces

scholarly journals DECOMPOSITION OF UNITARY MATRICES AND QUANTUM GATES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350015 ◽  
Author(s):  
CHI-KWONG LI ◽  
REBECCA ROBERTS ◽  
XIAOYAN YIN
Keyword(s):  
General Scheme ◽  
Quantum Gate ◽  
Quantum Gates ◽  
Unitary Matrix ◽  
Additional Structure ◽  
Unitary Matrices ◽  
Decomposition Scheme ◽  
Single Qubit ◽  
Matlab Program

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d - 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problems with the additional structural restrictions. A Matlab program is written to implement the scheme, and the result is used to deduce the fact that every quantum gate acting on n-qubit registers can be expressed as no more than 2n-1(2n-1) fully controlled single-qubit gates chosen from 2n-1 classes, where the quantum gates in each class share the same n - 1 control qubits. Moreover, it is shown that one can easily adjust the proposed decomposition scheme to take advantage of additional structure evolving in the process.

scholarly journals Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

2013 ◽  
Vol 61 (7) ◽  
pp. 1786-1796 ◽  
Author(s):  
Martin Kleinsteuber ◽  
Hao Shen
Keyword(s):  
Unitary Matrix ◽  
Joint Diagonalization
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